Respuesta :
Given:
Consider the given terms of the sequence are:
20, 10, 5, ...
To find:
The type of sequence (arithmetic or geometric) and the common difference / ratio in simplest form.
Solution:
We have,
20, 10, 5, ...
Difference between consecutive terms are:
[tex]10-20=-10[/tex]
[tex]5-10=-5[/tex]
Since [tex]-10\neq -5[/tex], therefore the given sequence has no common difference, it means the given sequence is not arithmetic.
Ratio between consecutive terms are:
[tex]\dfrac{10}{20}=\dfrac{1}{2}[/tex]
[tex]\dfrac{5}{10}=\dfrac{1}{2}[/tex]
The given sequence has a common ratio [tex]\dfrac{1}{2}[/tex], it means the given sequence is a geometric sequence.
Therefore, the given sequence is a geometric sequence with common ratio [tex]\dfrac{1}{2}[/tex] it is also written as 0.5.
